There are several strategies which can be employed in order to win your arguments.
One is to state your view then immediately run in circles with your fingers in your ears while shouting “la la la, not listening!” This can be very effective if you can sing very loudly (as can I), or you have plenty of stamina and a higher boredom threshold than those you are arguing against.
Another is to state that there’s no point trying to discuss something with someone whose mind is so obviously closed. This tactic provides no substance but is a useful exercise in meaningless point-scoring, and can sometimes lend an air of superiority to a stance which only really deserves attention from The Point And Laugh Brigade.
A better strategy is to ensure that your argument has a substantial logical basis and is presented in an appropriate way, and there are some books which can help you with this.
For a gently humorous exploration of the subject, you’ll not find better than Madsen Pirie’s How to Win Every Argument: The Use and Abuse of Logic. It’s an easy read; it’s entertaining, well-written, and witty; and it’s very informative.
Anthony Weston’s Rulebook for Arguments is a slim book which provides a slightly more serious read and discusses the various forms an argument can take.
If, however, you’re prepared to go really hard-core then The Trivium: The Liberal Arts of Logic, Grammar and Rhetoric by Sister Miriam Joseph is the book for you. It is dry and dense and at times almost impenetrable: I doubt it contains a single joke. But it’s rock-solid, rigorous, and absolutely reliable and if you’re brave enough to tackle it, it is a fascinating and transforming read.
What do any of these books have to do with publishing? Not much. But if a writer cannot formulate a coherent and logical argument then at best they’re going to make themselves look foolish and at worst they’re going to fail, no matter which genre they favour.